Complexity of relations in the braid group

Details Complexity of relations in the braid group Complexity of relations in the braid group

2009-05-31

arxiv.org/abs/0906.0137v1

Mathematics

Group Theory

Scientific paper

We show that for any given n, there exists a sequence of words a_k in the
generators sigma_1, ... sigma_{n-1} of the braid group B_n, representing the
identity element of B_n, such that the number of braid relations of the form
sigma_i sigma_{i+1} sigma_i = sigma_{i+1} sigma_i sigma_{i+1} needed to pass
from a_k to the empty word is quadratic with respect to the length of a_k.

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